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PubMed2000

Approximate entropy studies of hormone pulsatility from plasma concentration time series: influence of the kinetics assessed by simulation.

Approximate entropy (ApEn) is a method developed in the early nineties to quantify the "regularity" of a time series. In recent years, it has been vigorously employed to study the oscillatory/pulsatile secretory behavior of many hormones and found capable of successfully identifying pathological or prepathological states characterized by an enhanced secretion irregularity. Since hormone secretion rate is nonaccessible to direct measurement, ApEn is usually calculated from the time series of the hormone concentrations in plasma. However, the plasma concentration time course also reflects the whole-body kinetics of the hormone and can thus only provide a distorted portrait of the secretion rate at the gland level. In this paper, we investigate by simulation whether and how this distortion can influence the study of the regularity of hormone pulsatility by ApEn. Pulsatile secretion time series with different degrees of irregularity are simulated by varying the statistics of the random parameters which describe the secretory pulses. Then, plasma concentration time series are obtained by convolution with the hormone impulse response. Different degrees of impulse response smoothness are also considered in order to vary the amount of the distortion introduced. Results show that ApEn computed from secretion time series consistently discriminated better than ApEn calculated from plasma concentration time series among processes with different degrees of regularity. In addition, smoother impulse responses decreased the ApEn differences between plasma concentration time series corresponding to different degrees of secretion regularity. Therefore, the power of the ApEn index in the study of hormone pulsatility can potentially be enhanced by applying it to the hormone secretion time series.

Algorithms↗
PubMed2001

General strategy for hierarchical decomposition of multivariate time series: implications for temporal lobe seizures.

We describe a novel method for the analysis of multivariate time series that exploits the dynamic relationships among the multiple signals. The approach resolves the multivariate time series into hierarchically dependent underlying sources, each driven by noise input and influencing subordinate sources in the hierarchy. Implementation of this hierarchical decomposition (HD) combines principal components analysis (PCA), autoregressive modeling, and a novel search strategy among orthogonal rotations. For model systems conforming to this hierarchical structure, HD accurately extracts the underlying sources, whereas PCA or independent components analysis does not. The interdependencies of cortical, subcortical, and brainstem networks suggest application of HD to multivariate measures of brain activity. We show first that HD indeed resolves temporal lobe ictal electrocorticographic data into nearly hierarchical form. A previous analysis of these data identified characteristic nonlinearities in the PCA-derived temporal components that resembled those seen in absence (petit mal) seizure electroencephalographic traces. However, the components containing these characteristic nonlinearities accounted for only a small fraction of the power. Analysis of these data with HD reveals furthermore that components containing characteristic nonlinearities, though small, can be at the origin of the hierarchy. This finding supports the link between temporal lobe and absence epilepsy.

Algorithms↗
PubMedDate not supplied

Variational approaches toward nonlinear time-series analysis.

Linear autoregressive models (AR) have broad applications toward spectral analyses and digital filtering of signals, as well as identification, prediction, and control of dynamical systems. However, the symmetric Gaussian properties of linear AR presume independence between the first and second order moments of system outputs. Using nonlinear AR to quantify interactions between the mean and autocovariance of a signal, analysts can discriminate asymmetric frequency components, estimate the relative contribution of system nonlinearities toward mean output, evaluate relative structural stability of a system, and predict critical regions where bifurcations in its dynamics might occur. Quadratic analyses are performed on simulated outputs from a nonlinear model and various experimental time series (Canadian lynx population, respiratory volume dynamics in rat, Cheyne-Stokes respiration in patients with congestive heart failure, intracranial pressures in patient with cerebral hematoma). These case studies demonstrate the utility of the techniques for evaluating the qualitative behaviors of dynamical systems in the presence of slowly varying inputs.

Adult↗
PubMedDate not supplied

Noise factor analysis for cDNA microarrays.

A microarray-image model is used that takes into account many factors, including spot morphology, signal strength, background fluorescent noise, and shape and surface degradation. The model yields synthetic images whose appearance and quality reflect that of real microarray images. The model is used to link noise factors to the fidelity of signal extraction with respect to a standard image-extraction algorithm. Of particular interest is the identification of the noise factors and their interactions that significantly degrade the ability to accurately detect the true gene-expression signal. This study uses statistical criteria in conjunction with the simulation of various noise conditions to better understand the noise influence on signal extraction for cDNA microarray images. It proposes a paradigm that is implemented in software. It specifically considers certain kinds of noise in the noise model and sets these at certain levels; however, one can choose other types of noise or use different noise levels. In sum, it develops a statistical package that can work in conjunction with the existing image simulation toolbox.

Algorithms↗
PubMed2002

A calibration approach to glandular tissue composition estimation in digital mammography.

The healthy breast is almost entirely composed of a mixture of fatty, epithelial, and stromal tissues which can be grouped into two distinctly attenuating tissue types: fatty and glandular. Further, the amount of glandular tissue is linked to breast cancer risk, so an objective quantitative analysis of glandular tissue can aid in risk estimation. Highnam and Brady have measured glandular tissue composition objectively. However, they argue that their work should only be used for "relative" tissue measurements unless a careful calibration has been performed. In this work, we perform such a "careful calibration" on a digital mammography system and use it to estimate breast tissue composition of patient breasts. We imaged 0%, 50%, and 100% glandular-equivalent phantoms of varying thicknesses for a number of clinically relevant x-ray techniques on a digital mammography system. From these images, we extracted mean signal and noise levels and computed calibration curves that can be used for quantitative tissue composition estimation. In this way, we calculate the percent glandular composition of a patient breast on a pixelwise basis. This tissue composition estimation method was applied to 23 digital mammograms. We estimated the quantitative impact of different error sources on the estimates of tissue composition. These error sources include compressed breast height estimation error, residual scattered radiation, quantum noise, and beam hardening. Errors in the compressed breast height estimate contribute the most error in tissue composition--on the order of +/-7% for a 4 cm compressed breast height: The spatially varying scattered radiation will contribute quantitatively less error overall, but may be significant in regions near the skinline. It is calculated that for a 4 cm compressed breast height, a residual scatter signal error is mitigated by approximately sixfold in the composition estimate. The error in composition due to the quantum noise, which is the limiting noise source in the system, is shown to be less than 1% glandular for most breasts.

Adipose Tissue↗
PubMed2002

A framework for noise-power spectrum analysis of multidimensional images.

A methodological framework for experimental analysis of the noise-power spectrum (NPS) of multidimensional images is presented that employs well-known properties of the n-dimensional (nD) Fourier transform. The approach is generalized to n dimensions, reducing to familiar cases for n = 1 (e.g., time series) and n = 2 (e.g., projection radiography) and demonstrated experimentally for two cases in which n = 3 (viz., using an active matrix flat-panel imager for x-ray fluoroscopy and cone-beam CT to form three-dimensional (3D) images in spatiotemporal and volumetric domains, respectively). The relationship between fully nD NPS analysis and various techniques for analyzing a "central slice" of the NPS is formulated in a manner that is directly applicable to measured nD data, highlights the effects of correlation, and renders issues of NPS normalization transparent. The spatiotemporal NPS of fluoroscopic images is analyzed under varying conditions of temporal correlation (image lag) to investigate the degree to which the NPS is reduced by such correlation. For first-frame image lag of approximately 5-8%, the NPS is reduced by approximately 20% compared to the lag-free case. A simple model is presented that results in an approximate rule of thumb for computing the effect of image lag on NPS under conditions of spatiotemporal separability. The volumetric NPS of cone-beam CT images is analyzed under varying conditions of spatial correlation, controlled by adjustment of the reconstruction filter. The volumetric NPS is found to be highly asymmetric, exhibiting a ramp characteristic in transverse planes (typical of filtered back-rojection) and a band-limited characteristic in the longitudinal direction (resulting from low-pass characteristics of the imager). Such asymmetry could have implications regarding the detectability of structures visualized in transverse versus sagittal or coronal planes. In all cases, appreciation of the full dimensionality of the image data is essential to obtaining meaningful NPS results. The framework may be applied to NPS analysis of image data of arbitrary dimensionality provided the system satisfies conditions of NPS existence.

Algorithms↗
PubMed2003

Image reconstruction with shift-variant filtration and its implication for noise and resolution properties in fan-beam computed tomography.

In computed tomography (CT), the fan-beam filtered backprojection (FFBP) algorithm is used widely for image reconstruction. It is known that the FFBP algorithm can significantly amplify data noise and aliasing artifacts in situations where the focal lengths are comparable to or smaller than the size of the field of measurement (FOM). In this work, we propose an algorithm that is less susceptible to data noise, aliasing, and other data inconsistencies than is the FFBP algorithm while retaining the favorable resolution properties of the FFBP algorithm. In an attempt to evaluate the noise properties in reconstructed images, we derive analytic expressions for image variances obtained by use of the FFBP algorithm and the proposed algorithm. Computer simulation studies are conducted for quantitative evaluation of the spatial resolution and noise properties of images reconstructed by use of the algorithms. Numerical results of these studies confirm the favorable spatial resolution and noise properties of the proposed algorithm and verify the validity of the theoretically predicted image variances. The proposed algorithm and the derived analytic expressions for image variances can have practical implications for both estimation and detection/classification tasks making use of CT images, and they can readily be generalized to other fan-beam geometries.

Algorithms↗
PubMed2003

A new local multiscale Fourier analysis for medical imaging.

The Stockwell transform (ST), recently developed for geophysics, combines features of the Fourier, Gabor and wavelet transforms; it reveals frequency variation over time or space. This valuable information is obtained by Fourier analysis of a small segment of a signal at a time. Localization of the Fourier spectrum is achieved by filtering the signal with frequency-dependent Gaussian scaling windows. This multi-scale time-frequency analysis provides information about which frequencies occur and more importantly when they occur. Furthermore, the Stockwell domain can be directly inferred from the Fourier domain and vice versa. These features make the ST a potentially effective tool to visualize, analyze, and process medical imaging data. The ST has proven useful in noise reduction and tissue texture analysis. Herein, we focus on the theory and effectiveness of the ST for medical imaging. Its effectiveness and comparison with other linear time-frequency transforms, such as the Gabor and wavelet transforms, are discussed and demonstrated using functional magnetic resonance imaging data.

Algorithms↗
PubMed2003

A method for modifying the image quality parameters of digital radiographic images.

A new computer simulation approach is presented that is capable of modeling several varieties of digital radiographic systems by their image quality characteristics. In this approach, the resolution and noise characteristics of ideal supersampled input images are modified according to input modulation transfer functions (MTFs) and noise power spectra (NPS). The modification process is separated into two routines-one for modification of the resolution and another for modification of the noise characteristics of the input image. The resolution modification routine blurs the input image by applying a frequency filter described by the input MTF. The resulting blurred image is then reduced to its final size to account for the sampling process of the digital system. The noise modification routine creates colored noise by filtering the frequency components of a white noise spectrum according to the input noise power. This noise is then applied to the image by a moving region of interest to account for variations in noise due to differences in attenuation. In order to evaluate the efficacy of the modification routines, additional routines were developed to assess the resolution and noise of digital images. The MTFs measured from the output images of the resolution modification routine were within 3% of the input MTF The NPS measured from the output images of the noise modification routine were within 2% of the input NPS. The findings indicate that the developed modification routines provide a good means of simulating the resolution and noise characteristics of digital radiographic systems for optimization or processing purposes.

Algorithms↗
PubMed2004

Noise in flat-panel displays with subpixel structure.

Subpixel structures found in medical monochrome active-matrix liquid crystal displays (AMLCDs) affect noise estimates measured with conventional methods. In this work, we discuss methods that identify sources of noise and permit the comparison of luminance noise estimates across technologies independent of pixel design and device technology. We used a three-million pixel AMLCD with a pixel structure consisting of three color stripes, each in a two-domain, in-plane switching mode. Images of uniform fields displayed on the AMLCD were acquired using a low-noise, high-resolution CCD camera. The camera noise and flat-field response were characterized using a uniform light source constructed for this purpose. We show results in terms of spatial luminance noise and noise power spectrum for high-resolution images and for the same images processed with a pixel-aligned aperture. We find that the pixel-aligned aperture eliminates almost all the noise found in the high-resolution images, suggesting that most of the luminance noise in AMLCDs comes from the subpixel structure and less-than-100% aperture ratio, rather than from interpixel variations.

Computer Terminals↗
PubMed2004

On the noise variance of a digital mammography system.

A recent paper by Cooper et al. [Med. Phys. 30, 2614-2621 (2003)] contains some apparently anomalous results concerning the relationship between pixel variance and x-ray exposure for a digital mammography system. They found an unexpected peak in a display domain pixel variance plot as a function of 1/mAs (their Fig. 5) with a decrease in the range corresponding to high display data values, corresponding to low x-ray exposures. As they pointed out, if the detector response is linear in exposure and the transformation from raw to display data scales is logarithmic, then pixel variance should be a monotonically increasing function in the figure. They concluded that the total system transfer curve, between input exposure and display image data values, is not logarithmic over the full exposure range. They separated data analysis into two regions and plotted the logarithm of display image pixel variance as a function of the logarithm of the mAs used to produce the phantom images. They found a slope of minus one for high mAs values and concluded that the transfer function is logarithmic in this region. They found a slope of 0.6 for the low mAs region and concluded that the transfer curve was neither linear nor logarithmic for low exposure values. It is known that the digital mammography system investigated by Cooper et al. has a linear relationship between exposure and raw data values [Vedantham et al., Med. Phys. 27, 558-567 (2000)]. The purpose of this paper is to show that the variance effect found by Cooper et al. (their Fig. 5) arises because the transformation from the raw data scale (14 bits) to the display scale (12 bits), for the digital mammography system they investigated, is not logarithmic for raw data values less than about 300 (display data values greater than about 3300). At low raw data values the transformation is linear and prevents over-ranging of the display data scale. Parametric models for the two transformations will be presented. Results of pixel variance measurements made on raw data images will be presented. The experimental data are in good agreement with those of Cooper et al. It will be shown that the slope of 0.6 found by Cooper et al. for the log-log plot at low exposure is not due to transfer function nonlinearity, it occurs because of an additive variance term-possibly due to electronic noise. It will also be shown, using population statistics from clinical images, that raw data values below 300 are rare in tissue areas. Those tissue areas with very low raw data values are within about a millimeter of the chest wall or in very dense muscle at comers of images.

Breast Neoplasms↗
PubMed2004

How should low-contrast detail detectability be measured in fluoroscopy?

The relationship and precision of four methods for measuring the low-contrast detail detectability in fluoroscopic imaging were studied. These included the physical measurement of the accumulation rate of the square of the signal-to-noise ratio (SNR(rate)2), two-alternative forced-choice (2-AFC) experiments, sixteen-alternative forced-choice (16-AFC) experiments and subjective determination of the threshold contrast. The precision and sensitivity of the threshold contrast measurement were seen to be modest in the constancy testing of fluoroscopic equipment: only large changes in system performance could be reliably detected by that method. The measurement of the SNR(rate)2 is suggested instead. The relationship between the results of the various methods were studied, and it was found that human performance can be related to SNR(rate)2 by introducing the concept of the effective image information integration time (t(eff)). When measured for an unlimited observation time, it depicts the saturation of human performance in detecting a static low-contrast detail in dynamic image noise. Here, t(eff) was found to be about 0.6 s in 2-AFC tests and 0.3 s in 16-AFC tests.

Algorithms↗
PubMed2005

Evaluation of and compensation for spatial noise of LCDs in medical applications.

Recent developments in liquid crystal display (LCD) technology suggest that this technology will replace the cathode ray tube (CRT) as the most popular softcopy display technology in the medical arena. However, LCDs are far from ideal for medical imaging. One of the principal problems they possess is spatial noise contamination, which requires accurate characterization and appropriate compensation before LCD images can be effectively utilized for reliable diagnosis. This paper presents some work we have conducted recently on characterization of spatial noise of high resolution LCDs. The primary purpose of this work is to explore the properties of spatial noise and propose a method to reduce it. A high quality CCD camera was used for physical evaluation. Spatial noise properties were analyzed and estimated from the camera images via signal modeling and processing. A noise compensation algorithm based on error diffusion was developed to process images before they were displayed. Results shown in this paper suggest that LCD spatial noise can be effectively reduced via appropriate processing.

Algorithms↗
PubMed2005

Presampling, algorithm factors, and noise: considerations for CT in particular and for medical imaging in general.

CT scanners acquire noisy data at discrete sample positions. Typically, a convention of how to continue these data from discrete integer positions to the continuous domain must be applied during processing. We study the properties of three typical one-dimensional spatial domain interpolation algorithms in terms of a cost or quality factor Q. This figure of merit Q is a function of spatial resolution, data noise, and dose and is used to optimize detector design. Spatial resolution R is defined as either mean square width delta or as the full width at half maximum W of the point spread function (PSF). Our results show that a trapezoidal interpolation algorithm is optimal for the high resolution domain (relative to the detector aperture size g) and should be replaced by a triangular or Gaussian interpolation function for spatial resolutions of about 1.3g or larger; these result in bell-shaped PSFs. Assuming such a hybrid algorithm we find a 1.5-fold increase of Q2-this is equivalent to 50% improved dose usage-when smoothing the data to a spatial resolution of 3g or more compared to a highest resolution reconstruction. Therefore it is advisable to use detectors of one-third of the size of the desired spatial resolution W and to compensate for the 1.5-fold increase in Q2 by reducing dose by 33%. Under the presence of moderately sized septa (e.g., 10% of the spatial resolution element size) the benefit of optimizing still lies in the order of 30% improved dose usage; in that case the detector size g should be on the order of W/2 and a dose reduction of 23% can be achieved. Again, bell-shaped PSFs show a better tradeoff between noise and resolution for a given dose than rectangular-shaped PSFs. The general interpretation of our results is that the degree of freedom of choosing the weighting or interpolation function for a given resolution is large for small detectors and small for large detectors. Thus systems with small g have a higher potential of optimization compared to systems with large g. Similarly, detector binning, which corresponds to replacing g by 2g, should be avoided. Note that the figures reported correspond to a one-dimensional interpolation. Two-dimensional detectors typically separate and resulting quality factors can be easily obtained by multiplication. Then, Q2 is expected to improve by a factor of 1.52 without septa and by a factor of 1.32 with septa. This indicates that dose can be reduced by about 56% and about 41%, respectively. Our findings are general and not restricted to CT. They can be readily applied to medical or nonmedical imaging devices and digital detectors and they may also turn out to be useful in other fields.

Algorithms↗
PubMed2004

Improving generalization performance of natural gradient learning using optimized regularization by NIC.

Natural gradient learning is known to be efficient in escaping plateau, which is a main cause of the slow learning speed of neural networks. The adaptive natural gradient learning method for practical implementation also has been developed, and its advantage in real-world problems has been confirmed. In this letter, we deal with the generalization performances of the natural gradient method. Since natural gradient learning makes parameters fit to training data quickly,the overfitting phenomenon may easily occur, which results in poor generalization performance. To solve the problem, we introduce the regularization term in natural gradient learning and propose an efficient optimizing method for the scale of regularization by using a generalized Akaike information criterion (network information criterion). We discuss the properties of the optimized regularization strength by NIC through theoretical analysis as well as computer simulations. We confirm the computational efficiency and generalization performance of the proposed method in real-world applications through computational experiments on benchmark problems.

Algorithms↗
PubMed2004

Linear and nonlinear approaches to the analysis of R-R interval variability.

Analysis techniques derived from linear and non-linear dynamics systems theory qualify and quantify physiological signal variability. Both clinicians and researchers use physiological signals in their scopes of practice. The clinician monitors patients with signal-analysis technology, and the researcher analyzes physiological data with signal-analysis techniques. Understanding the theoretical basis for analyzing physiological signals within one's scope of practice ensures proper interpretation of the relationship between physiolgical function and signal variability. This article explains the concepts of linear and nonlinear signal analysis and illustrates these concepts with descriptions of power spectrum analysis and recurrence quantification analysis. This article also briefly describes the relevance of these 2 techniques to R-to-R wave interval (i.e., heart rate variability) signal analysis and demonstrates their application to R-to-R wave interval data obtained from an isolated rat heart model.

Animals↗
PubMed2003

[Bispectral analysis does not differentiate between anaesthesia EEG and a linear random process].

Bispectral analysis of the electroencephalogram (EEG) has been used to monitor depth of anaesthesia. In the majority of publications this has involved the use of the so called BIS-Index TM (Aspect Medical Systems, Inc.). The exact relationship of this index to such bispectral parameters as the bispectrum and bicoherence has not yet been reported. If the EEG is considered as a linear random process, bicoherence is trivial, i.e. it is independent of the EEG frequency. The aim of this study was to determine the proportion of EEG epochs with non-trivial bicoherence during isoflurane/N20 anaesthesia. We reanalyzed 25.5 hours of digitalised EEG signal from 9 patients undergoing gynaecological surgery. The test developed by Hinich for Gaussian distribution and linearity was then applied. The test was validated using various synthetic surrogate data: Gaussian random data, the z-component of the Lorenz attractor, the phase randomized EEG and the phase randomized z-component of the Lorenz attractor. The percentage of epochs (8.192 s, 1024 data points) with non-trivial bicoherence was: Lorenz data 95.4%, phase randomized Lorenz data 9.4%, synthetic Gaussian data 14.8%, original EEG 9.1%, phase randomized EEG 5.1%. The original EEG data were not found to contain a higher percentage of epochs with non-trivial bicoherence than the phase randomized data and the synthetic Gaussian data. We conclude that bispectral analysis does not substantially add to the information obtained with other methods of quantitative EEG analysis.

Adult↗
PubMed2004

Delay-dependent robust H infinity control for a class of uncertain switched systems with time delay.

For linear switched system with both parameter uncertainties and time delay, a delay-dependent sufficient condition for the existence of a new robust H infinity feedback controller was formulated in nonlinear matrix inequalities solvable by an LMI-based iterative algorithm. Compared with the conventional state-feedback controller, the proposed controller can achieve better robust control performance since the delayed state is utilized as additional feedback information and the parameters of the proposed controllers are changed synchronously with the dynamical characteristic of the system. This design method was also extended to the case where only delayed state is available for the controller. The example of balancing an inverted pendulum on a cart demonstrates the effectiveness and applicability of the proposed design methods.

Algorithms↗